Okay this is rather easy really.
Obviously you have two things to consider. The phone itself and the service.
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The phone.
This is going to be a biased point of view because we own the LTE so...
IMHO the Evo LTE is better than the X One from what I have read about them. For me it is mainly the Micro SD slot. We have 2 GB of app storage but the phone has another 12 GB to move apps to like we used to do on the old Evo to just the SD card. This frees up even more room on an additional 32GB card that I can put movies, music, tons of books (large PDF's even) and whatever I want. So basically I have 44GB between the 12GB internal and 32Gb card. That is a lot of storage. You could also swap SD cards if you really had to. It is rather easy to get to the SD slot on this one. I LOVE having an SD slot! The camera on this is AWESOME. unsure about the X One here so...
This phone is slim, fast and has a gorgeous screen. I look at people iPhones and think man is that small, how can you use that thing. So far this phone beats the living crap out of an iPhone. I am talking beat down, kicking it in the gut while it squirms in the dirt better.
I would easily bet that the next iPhone will have a larger screen. They have to to compete now. Apple is behind.
I only have one complaint about the EVO LTE so far and that is having the damn USB connector on the side. I much prefer it on the bottom but that is all personal opinion and does not take away from the phone.
I have not played with an X One but not read about any advantages over the LTE. The LTE seems equal or better in every area.
So you first have to decide which phone you prefer. If it is truly a toss up then only go by the service. So far for me +1 Sprint/LTE
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Service.
This is important. There are three things to consider here. Coverage, price and speed.
Coverage:
If your area has ty Sprint coverage then you probably want to go with AT&T. I personally hate AT&T and would rather go Verizon if I had to choose something other than Sprint. I LOVE Sprint though and will be a member for life unless they start pissing around with the data plans or I travel and need better coverage. So far Sprint is WAY ahead of the others for me at least.
If you have a good/equal Sprint area then +1 for Sprint. If you travel or move from one coverage area to the next and need better +1 Verizon.
Speed:
AT&T beats Sprint hands down here until Sprint's LTE service kicks in. I never really used the 4G option on my Evo. It sucked battery worse than anything. I personally never had any issues on plain old 3G. It is speedy enough for my normal phone usage and even when tethering my laptop web pages load just fine. I do not download large files or play a lot of video when I tether so...
+1 AT&T here overall because you simply cannot compare until Sprint's LTE kicks in. IF it ever does.
Price:
Hell we all know that Sprint kicks everyone ass here. So far customer service has been great for me. My coverage is fine so no extra roaming charges or problems for me.
If you use a lot of data then Sprint wins hands down as the others will just keep charging you.
If you only use a "normal" (under 2GB/month) amount of data and don't mind paying more each month then AT&T would be okay but it still looses simply because the plans on Sprint are much better!
+1 Sprint
BTW I have NEVER had even one call drop due to my end on Sprint. I talk to a friend most mornings as we both drive to work and he has AT&T and his calls are always having issues. I know it is not me because sometimes I am sitting still while he is moving in his car.
I also park in an underground garage surrounded in cement. I still get a full signal even at the bottom of the garage!
So go down the list and check off what is important to you and you will have your answer.